A body of mass m is projected horizontally with a velocity v from the top of a tower of height h and it reaches the ground at a distance x from the foot of the tower. If a second body of mass 2m is projected horizontally from the top of a tower of height 2h, it reaches the ground at a distance 2x from the foot of the tower. The horizontal velocity of the second body is :

Options

A. v
B. 2v
C. `sqrt2v`
D. `v/2`

Answer

C

Explanation

For the first body , ` h = 1/2 "gt"^(2)" "...(i)`
and `x = vt " "...(ii)`
From equations (i) and (ii) , we get
For the second body , let v.. be the velocity of projection. Then
`2h=1/2g((2x)^(2)/(v.^2))" "....(iv)`
Dividing equation (iii) by equation (iv) , we get